a heat transfer analysis of the fiber placement composite ...869-888).pdfclassified into two...

A Heat Transfer Analysis of the Fiber PlacementComposite Manufacturing Process

NOHA HASSAN, JOSEPH E. THOMPSON AND R. C. BATRA

Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State University

Blacksburg, VA 24061, USA

A. BRUCE HULCHER

NASA Marshall Space Flight CenterHuntsville, AL 35812, USA

XIAOLAN SONG

Materials Technology Center Southern Illinois UniversityCarbondale, IL 62901, USA

ALFRED C. LOOS*

Department of Mechanical EngineeringMichigan State University

East Lansing, MI 48824, USA

ABSTRACT: A computer code is developed to accurately simulate the three-dimensional heattransfer during the thermoset fiber placement composite manufacturing process. The code is basedon the Lagrangian formulation of the problem. Eight-node brick elements are employed, and the2� 2� 2 integration rule is used to numerically evaluate the integrals over an element. The coupledordinary differential equations obtained by the semidiscrete formulation of the problem areintegrated by the unconditionally stable backward difference method. The code is validated bycomparing the computed results for several problems with those available in the literature.Composite rings are manufactured by continuously laying a tape over a cylindrical mandrel and thetemperature histories at several points are measured with thermocouples. The computed temperaturedistribution is found to compare well with the test findings. The code can be used to optimize theprocessing variables.

KEY WORDS: fiber placement, finite element analysis, manufacturing.

INTRODUCTION

THE PROCESS MODELED here consists of laying down a unidirectional prepreg tapeon the surface of a mold by a moving head comprised of a heater and a roller

*Author to whom correspondence should be addressed. E-mail: [email protected]

Journal of REINFORCED PLASTICS AND COMPOSITES, Vol. 24, No. 8/2005 869

0731-6844/05/08 0869–20 $10.00/0 DOI: 10.1177/0731684405047773� 2005 Sage Publications

(see Figure 1). The former supplies the heat and the latter, the required pressure. Theconsolidation head moves with a speed V, which causes the temperature and stressvariations to be induced in the part being manufactured as a function of time and position.

A number of heat transfer models have been proposed for investigating the thermalhistory of fiber placement [1–10] and filament winding [11–16]. The techniques used areclassified into two categories. In the first one, a quasi-steady state is assumed to prevailthroughout the process, and the steady-state heat transfer problem in the Eulerianframework [1–5,9–13] is analyzed; and the transient heat conduction equation in theLagrangian framework [6–8,14–16] is solved in the second.

Grove [1] developed a two-dimensional finite element (FE) model to investigate thetemperature profile of the tape laying process with a single laser heat source. The regionclose to the tape–substrate interface was modeled using a coordinate system fixed to the lay-up head and moving with it. Thus, the problem could be solved by using a fixed FE mesh.Furthermore, the movement of the lay-up head was modeled by incrementally shifting thecalculated temperature distribution throughout the mesh at appropriate time intervals.Nejhad et al. [3,9] used a finite difference (FD) method to show that very high temperaturegradients existed near the nip point, and that the roller speed, heat input, and preheatingsignificantly affected the temperature field in the laminate. A control volume, whichincludes the region influenced by the local heat source, was chosen and the problem wasformulated as steady-state using an Eulerian approach. Results were computed for a flat-bed fiber placement process [3] modeled as a two-dimensional problem, and for the filamentwinding process [9] modeled as a three-dimensional problem. James and Black [11,12]investigated the continuous filament winding process employing an infrared energy source.They also transformed the transient thermal problem into a quasi-steady one in an Eulerianframe. The one-dimensional heat transfer analysis of the tape regime was coupled to thethree-dimensional heat transfer analysis of the composite–mandrel assembly. The explicitFD method was used to solve the problem numerically. For both the fiber placement andthe filament winding processes, a point in the laminate experiences a series of thermalimpulses (rapid heating followed by slower cooling), which decreases in magnitude assuccessive plies are added [1]. Sonmez and Hahn [4,5] investigated the temperature historyand the crystallinity developed during subsequent lay-ups of the fibers. Loos and Song [13]have computed thermal histories at a point in a filament wound composite ring.

Figure 1. Schematic diagram of the tape laying process.

870 N. HASSAN ET AL.

Springer and his coworkers [6,7,14] have developed the two-dimensional thermo-chemical models to ascertain the temperature, the degree of cure (for thermosetting matrixcomposites) or the crystallinity (for thermoplastic matrix composites), and viscosity insidethe composite for both tape laying and filament winding processes. The lay-up process wassimplified by assuming that the top layer is laid down instantaneously along the entirelength of the composite and the lay-up head then moves along the top surface of the layerto consolidate it onto the substrate. The time history of the thermochemical variables wascomputed by the FE method. An implicit backward difference method was used tointegrate, with respect to time t, the coupled ordinary differential equations arising fromthe semidiscrete formulation of the problem. Pitchumani et al. [8] also used the two-dimensional transient heat transfer model to optimize the thermoplastic tow-placementprocess. Shih and Loos [15,16] used the commercial FE package, ABAQUS, to study thetransient heat transfer problem associated with a continuous filament winding processusing a hot-air heater. Assuming that very little energy propagates across the interfacebetween the compaction roller and the composite substrate, they found the temperatureprofile in the substrate cylinder and the towpreg prior to its reaching the nip-point.

We note that the problem is really three-dimensional since during continuous placementof the towpreg, heat is conducted in all the three directions. Here we present such a modelwith the following unique features: (i) continuous laying of the tape rather than the entirelayer being laid down instantaneously and (ii) three-dimensional heat transfer problemincluding heat conduction in the tool and heat exchange through convection with thesurroundings.

FORMULATION OF THE PROBLEM

A mold with its upper surface partially covered by the prepreg tape of width w is shownin Figure 2. During the ensuing time interval �t, a piece of tape of length �l is laid next tothe end of the prepreg tape and thermal energy at the rate _QQ is supplied to this piece and toa small area surrounding it. The size of this area depends upon the speed of hot air comingout of the heater nozzle, the distance of the nozzle from the mold, and the inclination ofthe heater nozzle with respect to the mold. The speed V of the moving head equals �l/�t.After the entire top surface of the mold has been covered with the towpreg tape, thedirection of tape placement is reversed. That is, the towpreg moves West from the

MOLD

A B

C D

∆l

Figure 2. Mold with the top surface partially covered by the prepreg tape.

Heat Transfer Analysis of Composite Manufacturing Process 871

Northeast corner. The goal is to find the temperature distribution as a function of time t;hence the mold and the prepreg tape are regarded as rigid bodies.

The heat transfer is governed by the transient heat conduction equation with heatgeneration:

�cp _TT � kijT, j

� �, i� _QQ1 � _QQ2 ¼ 0 in �, ð1Þ

where � is the mass density, cp the specific heat, _TT the rate of change of temperature at amaterial point, kij the thermal conductivity tensor, _QQ1 the rate of heat generated per unitvolume due to exothermic chemical reactions that occur during curing of the resin, _QQ2 therate of energy supplied to a unit volume of the prepreg tape by the heat source, and � isthe region of space occupied by the body. Here T, i ¼ @T=@xi, _TT ¼ DT=Dt ¼ @T=@t sincewe are using the Lagrangian description, and a repeated index implies summation over therange of the index.

The boundary conditions include either prescribed temperatures, or heat transfer due toconvection. That is

T ¼ T̂T on �u, ð2Þ

�kijT, jni ¼ h T � T1ð Þ on �t, ð3Þ

where T̂T is the prescribed temperature, h is the coefficient of convective heat transfer, n isan outward unit normal to the surface, and T1 is the ambient temperature. �u and �t areparts of the boundary � of � where the temperature and the heat flux are prescribed,respectively. For a thermally insulated surface, h¼ 0. The value of h is a function of thehot air speed and possibly its temperature; however, it is taken to be a constant here.

The material of the prepreg tape is assumed to be orthotropic. For the coordinate axesaligned with the material principal axes, the conductivity matrix kij is diagonal. When theaxes of material symmetry in the plane of the tape make an angle � with the global x1 andx2 axes, and the transverse direction of the tape is along the x3-axis, the nonzero terms inthe conductivity matrix are

k11 ¼ kL cos2 � þ kT sin2 �, ð4Þ

k12 ¼ kL � kTð Þsin � cos �, ð5Þ

k22 ¼ kL sin2 � þ kT cos2 �, ð6Þ

k33 ¼ kT : ð7Þ

Here kL and kT denote respectively the thermal conductivities along the length of thefiber and perpendicular to it.

The essential boundary condition (2) is imposed on the bottom surface of the mold, andnatural boundary conditions (3) are applied on the remaining bounding surfaces of thecomposite body. Note that the edge BC of the prepreg tape will occupy a different positionin space as the next piece of the prepreg tape is laid down.

The prepreg tape is assumed to contain a thermosetting polymeric resin. An increasein temperature causes the resin to cure, and heat is generated by exothermic chemicalreactions during the curing of the resin.


On the assumption that the rate of heat generation during cure is proportional to therate of the cure reaction, the degree of cure, ��, of the resin can be defined as

�� ¼HðtÞ

HR, ð8Þ

where H(t) is the heat evolved from the beginning of the reaction to the present time t, andHR is the total heat of reaction during complete cure of the resin. Differentiation ofEquation (8) with respect to time and the rearrangement of terms give

_HH ¼d ��

dtHR ð9Þ

where d ��=dt is the reaction or the cure rate. An expression for the cure rate of athermosetting resin, which is a function of temperature and degree of cure, is

d ��

dt¼ f T , ��ð Þ 1� ��ð Þ

nð10Þ

where the function f T , ��ð Þ depends on the type of reaction and n is the reaction order. Thefunction f is usually of the form:

f T , ��ð Þ ¼ k1 þ k2 ��m ð11Þ

where k1 and k2 are the rate constants, and m is a kinetic exponent. The temperaturedependence of the rate constants is given by an Arrhenius-type expression:

ki ¼ Aiexp�Ei

RT

� �, i ¼ 1, 2, ð12Þ

where Ai is the Arrhenius pre-exponential factor, Ei the Arrhenius activation energy, andR the gas constant. Values of these constants can be found by using a procedure similarto that given in [17]. If diffusion of chemical species and convection of the fluid areneglected, then the degree of cure at each material point can be determined by integratingthe cure rate with respect to time.

NUMERICAL SOLUTION

The three-dimensional heat transfer problem formulated above is solved by the finiteelement method. The domain of study is discretized into eight-node brick elements. TheGalerkin approximation of the problem is derived as follows:

Multiplication of both sides of Equation (1) by a test function � that vanishes on �u,integration of the resulting equation over the domain �, and the use of the divergencetheorem give

Z�

�cp _TT� d�þ

Z�

kijT, j�, i d�þ

Z�t

hT� d� ¼

Z�t

hT1� d�þ

Z�

� _QQ1 þ _QQ2

� �d�: ð13Þ


Recall that

Z�

ð�Þ d� ¼Xe

Z�e

ð�Þ d� ð14Þ

where �e is an eight-node brick element in �. On an element �e, the temperature isassumed to be given by

T x1, x2, x3, tð Þ ¼P8A¼1

NA x1, x2, x3ð ÞTAðtÞ,

� x1, x2, x3ð Þ ¼P8A¼1

NA x1, x2, x3ð ÞCA,

ð15Þ

where N1,N2, . . . ,N8 are shape functions, T1,T2, . . . ,T8 are time-dependent temperaturesof eight-nodes, and C1,C2, . . . ,C8 are constants. Substitution from Equations (14) and(15) into Equation (13) and recalling that the function � is arbitrary we arrive at thefollowing set of coupled ordinary differential equations for the determination of the nodaltemperatures:

M _TTþ KT ¼ F: ð16Þ

Here

M ¼Xe

Me, K ¼Xe

Ke, F ¼Xe

Fe,

MeAB ¼

Z�e

�cpNANB d�,

KeAB ¼

Z�e

kijNA, jNA, i d�þ

Z�t\�e

hNANB d�,

FeA ¼

Z�t\�e

hT1NA d�þ

Z�e

NA_QQ1 þ _QQ2

� �d�:

ð17Þ

M is the heat capacity matrix, K is the conductivity matrix, and F is the load vector.The coupled ordinary differential equations (16) are integrated for nodal temperatures

by an unconditionally stable backward difference scheme. For a given speed of the movinghead, the time step size �t used in the backward difference integration scheme is related tothe length �l of the piece of the prepreg tape just being laid down. Both �t and �l can beadjusted to compute the temperature field within the prescribed accuracy. The applicationof the backward difference formula to Equation (16) results in a system of simultaneouslinear algebraic equations for the nodal temperatures. Essential boundary conditions areenforced by the penalty method and equations are solved for nodal temperatures.

A three-dimensional finite element code, FBPLACE, is written in the modular formto simulate the fiber placement process. The code solves the system of equations governingthe heat transfer and incorporates heat generated due to curing and different types ofboundary conditions. It uses eight-node brick elements, the eight-point Gauss integration


rule, and the lumped mass matrix. A direct sparse solver is used to solve the set of linearalgebraic equations. The code has a data base of material models that contains values ofvarious material parameters needed for each analysis. Input and output formats for allmodels are based on the neutral file concept of the solid modeling package PATRAN. Thecode has been verified by comparing the computed results for several problems with theiranalytical solutions; an example is given here.

Consider the transient heat conduction in a rod of 1m length with no heat generation.The temperature at the left end of the bar is specified to be zero and a convectionboundary condition is applied to the right end of the rod. That is,

T ¼ 0 x ¼ 0, t � 0

�k@T

@x¼ hðT � 0Þ x ¼ 1, t � 0

ð18Þ

The initial temperature distribution in the rod is expressed as

Tt¼0 ¼4000x 0 � x � 0:025

100 0:025 � x � 1:0

(ð19Þ

The problem can be solved by the method of separation of variables as given in [18].The finite element solution was compared with the analytical solution of the problem inFigure 3. It is clear that the two solutions essentially coincide with each other.

For the tape laying process, the three-dimensional temperature distribution in the tapeelement and the mold were computed with FBPLACE and the commercial code ABAQUSafter only one element had been placed on the mold. Again the two solutions were foundto agree with each other.

Figure 3. Comparison of the finite element and the analytical solutions of heat conduction in a bar.


EXPERIMENTAL

In order to validate and verify the theoretical model, composite rings weremanufactured by laying a prepreg tape on a cylindrical mandrel. Except for the differencein the geometry, this process has all the ingredients of the one used to manufacture flat andcurved parts. Critical parameters include the heat supplied to the prepreg tape and thepressure applied at the nip point. Heating the prepreg tape causes the resin to soften andflow, which permits deformation of the resin-saturated fiber tow. Overheating of theprepreg during lay-up will result in too much resin flow and excessive nip point pressurecan cause large transverse deformation.

The fiber placement facility is schematically illustrated in Figure 4 and includes aprepreg delivery system, a computer-controlled filament winding machine, and aconsolidation head assembly. Figure 5 shows a photograph of the consolidation headassembly. The prepreg enters from the right from the tension controller, and passesthrough the two white Teflon and two aluminum guide rollers before exiting onto themandrel surface. The large black cylinder between the two sets of rollers is an infraredthermometer and is used to measure the surface temperature of the incoming prepreg. Thehorizontal silver cylinder toward the bottom of the crosshead is a pneumatic cylinderattached to the 25.4mm (1 in.) diameter steel compaction roller. The cylinder can producea nip-point force of 442.2N (99.4 lb) at 689.5 kPa (100 psi) air pressure. The cylindricalcomponent located at the upper left hand corner of Figure 5 is the hot gas heater. Dry,compressed air is heated and ejected through the nozzle at the bottom. The maximum airtemperature is 870�C (1600�F). At the end of the armored cable leading to the nozzle is thethermocouple that reads the exiting air temperature. The air temperature is controlled bya proportional integral derivative controller. The aluminum mandrel is 146mm (5.75 in.)in diameter and 152.4mm (6 in.) in length.

The filament winding machine is able to control spindle rotation and linear carriagemotion. A personal computer is used to provide supervisory control, display information,and store and load the machine’s motion and control program. Winding patterns aregenerated off-line by CADWINDTM pattern generation software.

Figure 4. Illustration of the fiber placement facility.


An in situ measurement system was constructed to acquire thermal data during thelay-up process. The temperature measurements during fiber placement were obtained byusing a nine-channel slip ring assembly installed on the spindle of the mandrel. Figure 6shows several thermocouples embedded in the composite lay-up. For this project, amaximum of eight K-type, fast-responding thermocouples were used. Because of the rapid

Figure 5. Consolidation head assembly.

Figure 6. Thermocouples embedded in the composite ring during lay-up.


temperature changes during the process, a data acquisition with a high sampling rate wasrequired. A PC-based data acquisition (DAQ) system was selected which consisted ofthe computer, the SCXI signal conditioning modules, the DAQ board, and NationalInstruments’ LabVIEW software. Additional details of the fiber placement and dataacquisition systems can be found in [21].

Composite specimens were fabricated from Cytec-Fiberite IM7/977-2, graphite fiber/epoxy resin slit tape. The uncured towpreg was 3.175mm wide and 0.16mm thick. Thecomposite lay-ups were 32 plies thick and were wound on an aluminum mandrel with anouter diameter of 146mm (5.75 in.). All of the composite rings were hoop wound and wereeither 3.175mm or 25.4mm in length.

The parameters that can be directly controlled during lay-up are heater air temperature,heater airflow rate, mandrel speed, roller pressure, and distance between the heater nozzleand the nip point. Of these, the heater airflow rate and distance from the nozzle to the nippoint were fixed and held constant for ring production. Heater gas temperature, mandrelspeed, and roller pressure were varied.

The baseline parameters that were selected were as follows. A temperature of 121�C(250�F) was found to provide adequate resin flow under compaction without adhering tothe roller. A pressure of 345 kPa (50 psig) applied to the compaction roller was foundto yield good compaction without excessive deformation of the composite substrate. Themandrel speed was found to be inconsequential compared to the roller pressure and heatergas temperature. A standard speed of 6 rpm was chosen. The pressure of the air suppliedto the heater was set at 55 kPa (8 psig). The distance from the nozzle of the heater to thenip point, and the angle of the heater were set to provide uniform heating of the prepregand composite substrate at the nip point while maintaining sufficient clearance betweenthe nozzle and the composite.

RESULTS

In simulating the fiber placement process, the motion of the fiber placement head mustbe considered. The computer code FBPLACE uses the Lagrangian description in whichone follows a set of fixed material particles. The hot gas heater, modeled as a convectiveboundary condition, moves along the mandrel–composite substrate. The speed of the headis modeled by incrementally moving the heat source around the outer surface of thecomposite as shown in Figure 2. The computational procedure is as follows:

1. Construct a finite element mesh of the tool and the entire composite laminate;2. Initially, at time equal to zero, apply boundary conditions to the tool only;3. At each time step, add a new composite element;4. Modify the boundary conditions as each new element is added;5. Calculate the temperature distribution at each time step; and6. Once the temperature distribution is known, calculate the resin degree of cure.

Figure 7 shows the finite element mesh (mesh 1) of the composite ring and the entiremandrel assembly. The aluminum mandrel has an inner diameter of 134 mm, an outerdiameter of 146mm, and is 152.4mm long. There are three layers of elements through thethickness, 32 elements in the circumferential direction, and 48 elements along the lengthfor a total of 4608 elements. For the composite lay-up, there are 32 layers of elementsthrough the thickness. Each layer is 0.16mm thick and 3.175mm wide. A total of 1024elements were used to represent the composite.


The finite element mesh of the entire aluminum mandrel and composite ring is quitelarge. In order to reduce the computation time required for a complete windingsimulation, a mesh with a reduced number of elements was generated as shown in Figure 8(mesh 2). The simplified mesh includes only the portion of the mandrel that the compositering is wound onto and the number of elements is reduced to 1120.

Figure 7. Finite element mesh for the composite ring and the entire mandrel (mesh 1).

Figure 8. Finite element mesh for the composite ring and section of the mandrel (mesh 2).


The temperature versus time profiles for the two finite element meshes are compared inFigure 9 for a single point at the mandrel–composite interface. From the figure it can beseen that the temperature versus time profiles are almost identical for the two meshes. Thetemperatures at other points within the composite lay-up compared well for the twomeshes. Henceforth, the smaller of the two meshes (mesh 2) was used for the remainingsimulations.

The surface area of the mandrel impinged upon by the hot air was determined asfollows: Eight equally spaced thermocouples were mounted both in the axial and in thecircumferential directions on the mandrel. Hot air from the heater was blown on themandrel and readings of the thermocouples were recorded. It was estimated that the hotair affected a circular region of radius 9.5mm centered at the center of the air nozzle.During the computation of results presented here, the temperature of the hot air and theheat transfer coefficient, h, between it and the mandrel and that between the hot air andthe prepreg tape were assumed to be the same constants. Furthermore, h was taken to beindependent of the temperature.

Figure 10 shows the calculated temperatures as a function of time during lay-up of a32-ply thick composite ring using the baseline processing parameters. The temperatures ofpoints in layers 2, 10, 20, and 30 are shown. The temperature is the highest when the layeris initially wound onto the composite substrate and then gradually decreases with time asadditional layers are added to the composite. Note that the peak temperature of the toplayer increases as the thickness of the composite increases and it becomes closer to thenozzle of the hot gas heater. This is because the towpreg is now being laid over a warmersubstrate and also the temperature of the air impinging on it is a little higher because of theslightly smaller distance between the nozzle and the composite part.

Thermocouples were embedded in different layers during the manufacturing process.Figure 11 exhibits locations of four thermocouples used in the experiment. Note that thethermocouples are mounted on the surface of the mandrel. The value of the convective

20

22

24

26

28

30

32

34

36

100 150 200 250 300 350Time, t, seconds

Tem

pera

ture

, T, o C

Computed - Mesh 1

Computed - Mesh 2

0 50

Figure 9. Comparison of the temperature vs time profiles for the two meshes.


heat transfer coefficient used in the simulation model was estimated by assuming a valueand comparing the temperature versus time profiles with the measured values. Thisprocess was repeated until the predicted temperature profile agreed with the measuredprofile. The results for two measured temperature locations are shown in Figure 12 forthermocouple 6 and Figure 13 for thermocouple 7. From the results it can be concludedthat simulations with a convection coefficient of 350W/m2 �C predicted temperatures thatwere closest to the measured values.

Three additional simulations were performed to verify the model and delineate the effectof the winding speed and the hot air temperature on the composite temperature. Shown inTable 1 are the values for the parameters that were varied. A convection coefficient of350W/m2 �C was used for all the simulations.

Figure 10. Layer temperatures as a function of time during lay-up of a 32-ply composite ring.

Figure 11. Thermocouple locations on the surface of the mandrel.


Figure 12. A comparison of computed and measured temperatures at thermocouple 6 for different values ofthe convective heat transfer coefficient.

Figure 13. A comparison of computed and measured temperatures at thermocouple 7 for different values ofthe convective heat transfer coefficient.


The computed and measured temperature versus time history at thermocouple location 5is shown in Figure 14 for the baseline processing conditions (Case 1). Except for windingof the first layer, the peak predicted temperatures match the measured values very well.Overall, there is good agreement between the calculated and measured temperature versustime profiles for the 32 layers. The effect of reducing the winding speed on the temperatureversus time profile can be observed by comparing data in Figures 14 and 15. At the lowerwinding speed of 3 rpm, the measured peak temperatures during winding of the first fourlayers were as much as 10�C higher than predicted. This is most likely due to the transienteffects during the beginning of the winding process. After layer number four, thecalculated and measured peak temperatures match very well. Note that after about 100 s,the measured temperature versus time history begins to lead the calculated history. By theend of the winding process, the measured temperature versus time history is one completecycle ahead of the predicted temperature versus time history. This is due to the poorcontrol of the mandrel speed at low rpm. At the end of the winding process, the peaktemperatures are about 33 and 35�C for winding speeds of 6 and 3 rpm, respectively.

The effect of increasing the hot gas heater air temperature can be observed bycomparing the results given in Figures 14 and 16. An increase in the air temperature of20�C results in about a 3�C rise in the peak temperature at a point in the composite.

Thermocouple "5"

20

25

30

35

40

45

0 50 100 150 200 250 300 350Time, t, seconds

Tem

pera

ture

, T, o C

Computed- CASE 1

Experimental-CASE 1

Figure 14. A comparison of the computed and the measured temperature vs time histories at the location ofthermocouple 5 for case 1.

Table 1. Parametric studies.

CaseAir temperature

(�C)Winding speed

(rpm)

1 121 62 121 33 150 6


Figure 17 exhibits the temperature variation in the radial direction within the compositecylinder at the conclusion of manufacturing a 32-layer composite ring. The temperaturevaries very gradually within the mandrel since it is a good conductor of heat but variesrapidly in the composite cylinder. However, the temperature difference between theoutermost and the innermost layers is less than 2.4�C. If the temperature variation in the


Thermocouple "5"

15

20

25

30

35

40

45

50

0 100 200 300 400 500 600 700

Time, t, seconds

Tem

pera

ture

, T, o C

Computed- CASE 2

Experimental-CASE 2



manufactured part is taken as an indicator of the quality of the part produced, then the32-layer ring should be of good quality.

The placement of a prepreg tape on the surface of a sine wave tool was simulated withthe computer code FBPLACE. Figure 18 shows the finite element mesh for the 1m longand 0.5m wide aluminum tool divided into 1600 elements. The composite laminate was8 plies thick and had 400 elements per ply.

The cure kinetics model for Hexcel AS4/3501-6 carbon/epoxy prepreg was used in thesimulations [22]. Figure 19 depicts time histories of the temperature and the degree of cureat the point located at the geometric center of layer 1. Note the eight temperature spikesin the figure. The spike occurs first during initial lay-up of the towpreg (the highesttemperature predicted) and then seven more times as subsequent layers are placed and thehot gas torch passes over the first layer. At the end of the fiber placement, a degree of cureof 0.076 is predicted. Figure 20 shows the degree of cure distribution in layer 1 after thecompletion of the lay-up process. Information on the degree of resin cure in the compositeafter lay-up is important in assessing if the resin is sufficiently staged so that the hightemperature cure can proceed without excessive resin flow.

Figure 17. Radial temperature distribution at the completion of the winding process.

Figure 18. Finite element mesh for the sine wave tool and the composite laminate.


Figure 20. Distribution of the degree of cure in layer 1 upon completion of fiber placement.

Time (min)

0 200 400 600 800 1000

Tem

pera

ture

(o C

)

20

25

30

35

40

45

50

Deg

ree

of c

ure

0.00

0.02

0.04

0.06

0.08

TemperatureDegree of cure

History of temperature and cure for centerpoint of layer 1Figure 19. Time history of the temperature and the degree of cure at the geometric center of the top layer.


CONCLUSIONS

A major objective of the research program was to develop a comprehensive simulationmodel of the fiber placement composite manufacturing process. Initial work has focusedon modeling the two-step process commonly used today with thermoset prepreg tape.In the two-step process, the structure is cured in a separate step after lay-up.

A three-dimensional finite element code to analyze heat transfer in the tape layingprocess was developed. Unique features of the model are: (i) continuous laying of the taperather than the entire layer being laid down instantaneously and (ii) three-dimensionalheat transfer, including heat conduction in the tool and heat exchange through convectionwith the surroundings.

In order to validate and verify the theoretical model, composite cylinders weremanufactured by laying a prepreg tape on a cylindrical mandrel. The temperatures weremeasured during fiber placement by thermocouples embedded in the composite substrate.Overall, the measured temperatures agreed well with the model predicted values. Reasonsfor small differences between the measured and the computed results include (i)approximations made to estimate the heat transfer coefficient between the hot air andthe prepreg tape and that between the hot air and the tool surface, (ii) error in estimatingthe surface area of the cylinder affected by the hot air, (iii) thermal conductivities of theprepreg tape in three principal material directions, (iv) temperature of the hot airimpinging upon the tape and the tool, (v) neglecting of the increase in the temperature ofthe prepreg tape as it is laid on the composite substrate, (vi) neglecting heat conductedaway from the part being manufactured to the parts supporting the mandrel, (vii)variations in the mandrel speed, and (viii) neglecting the dependence of material propertiesupon the temperature. Future work will refine the model and consider these effects.

ACKNOWLEDGMENTS

The work was supported by the National Center for Advanced Manufacturing –Louisiana Partnership. Dr Bruce Brailsford, Technical Director of NCAM was the projectmonitor. The authors wish to thank Mr Randy S. Stevens of Lockheed Martin SpaceSystems Company – Michoud Operations for providing the prepreg materials.

REFERENCES

1. Grove, S. M. (1988). Thermal Modeling of Tape Laying with Continuous Carbon-Fiber-ReinforcedThermoplastics, Composites, 19: 367–375.

2. Beyeler, E. P. and Guceri, S. I. (1988). Thermal Analysis of Laser Assisted Thermoplastic-Matrix CompositeTape Consolidation, Journal of Heat Transfer, 110: 424–430.

3. Nejhad, M. N. G., Cope, R. D. and Guceri, S. I. (1991). Thermal Analysis of In-Situ ThermoplasticComposite Tape Laying, Journal of Thermoplastic Composite Materials, 4: 20–45.

4. Sonmez, F. O. and Hahn, H. T. (1997). Modeling of Heat Transfer and Crystallization in ThermoplasticComposite Tape Placement Process, Journal of Thermoplastic Composite Materials, 10: 198–240.

5. Sonmez, F. O. and Hahn, H. T. (1997). Analysis of the On-line Consolidation Process in ThermoplasticComposite Tape Placement, Journal of Thermoplastic Composite Materials, 10: 543–572.

6. Mantell, S. C., Wang, Q. and Springer, G. S. (1992). Processing Thermoplastic Composites in a Press and byTape Laying – Experimental Results, Journal of Composite Materials, 26: 2378–2401.


7. Sarrazin, H. and Springer, G. S. (1995). Thermochemical and Mechanical Aspects of Composite TapeLaying, Journal of Composite Materials, 29: 1908–1943.

8. Pitchumani, R., Gillespie, J. W. and Lamontia, M. A. (1997). Design and Optimization of a ThermoplasticTow-Placement Process with In-Situ Consolidation, Journal of Composite Materials, 31: 245–275.

9. Nejhad, M. N. G., Cope, R. D. and Guceri, S. I. (1991). Thermal Analysis of In-Situ ThermoplasticComposite Filament Winding, ASME Journal of Heat Transfer, 113: 304–313.

10. Nejhad, M. N. G. (1991). Issues Related to Processability During the Manufacture of ThermoplasticComposites Using On-Line Consolidation Techniques, Journal of Thermoplastic Composite Materials, 6:130–145.

11. James, D. L. and Black, W. Z. (1996). Thermal Analysis of Continuous Filament-Wound Composites,Journal of Thermoplastic Composite Materials, 9: 54–75.

12. James, D. L. and Black, W. Z. (1997). Experimental Analysis and Process Window Development forContinuous Filament Wound APC-2, Journal of Thermoplastic Composite Materials, 10: 255–276.

13. Loos, A. C. and Song, X. (2000). Thermal Modeling for the Consolidation Process of ThermoplasticComposite Filament Winding, In: Proceeding of the ASME Heat Transfer Division, HTS-Vol. 366-3, pp. 355–364, ASME, New York.

14. Mantell, S. C. and Springer, G. S. (1992). Manufacturing Process Models for Thermoplastic Composites,Journal of Composite Materials, 26: 2348–2377.

15. Shih, P. J. and Loos, A. C. (1999). Heat Transfer Analysis of the Thermoplastic Filament Winding Process,Journal of Reinforced Plastics and Composites, 18: 1103–1112.

16. Shih, P. J. and Loos, A. C. (1997). Design of Experiments Analysis of the On-Line Consolidation Process,In: Scott, M. (ed.), Proceedings of the Eleventh International Conference on Composite Materials, Vol. IV:Processing and Microstructure, pp. IV-92–IV-102, Australian Composite Structures Society, WoodheadPublishing Limited.

17. Grimsley, B. W., Hubert, P., Song, X., Cano, R. J., Loos, A. C. and Pipes, R. B. (2002). Effects of Amine andAnhydride Curing Agents on the VARTM Matrix Processing Properties, SAMPE Journal, 38(4): 8–15.

18. Ozisik, M. N. (1993). Heat Conduction, pp. 45–49.

19. Loos, A. C., Rattazzi, D. and Batra, R. C. (2002). A Three-Dimensional Model of the Resin Film InfusionProcess, Journal of Composite Materials, 36: 1255–1273.

20. Chamis, C. (1983). Simplified Composite Micromechanics Equations for Hygral Thermal and MechanicalProperties, In: 38th Annual Conf., The Society of Plastics Industry, Wiley-Interscience, New York, 2ndEdition, Vol. 21C, pp. 1–9.

21. Shih, P. J. (1997). On-Line Consolidation of Thermoplastic Composites, PhD Thesis, Virginia PolytechnicInstitute and State University, Blacksburg, VA 24061.

22. Lee, W. I., Loos, A. C. and Springer, G. S. (1982). Heat of Reaction, Degree of Cure and Viscosity ofHercules 3501-6 Resin, Journal of Composite Materials, 16: 510–520.


a heat transfer analysis of the fiber placement composite ...869-888).pdfclassified into two...

Documents